# Long term correction

The wind farm power predicted by Whiffle’s LES model strongly depends on the weather conditions during the simulation. For example; simulating a particularly windy period will yield a high power, and simulating a period with lots of stable situations will show a lot of wake effects. This way of modelling, which we also call ‘real-weather LES', gives deep insight into the atmospheric dynamics that govern the turbines' power production during the particular simulation time.

However, the output of an LES simulation of one year, or even shorter, gives no information about the long-term power production of the wind park (the annual energy production, AEP). To estimate the long-term AEP from a shorter LES simulation, therefore, we developed a method called *long-term correction*.
It works as follows: from a simulation conducted in Whiffle Wind, we extract the probability distributions of each turbine’s power production. We then calculate the statistical relationships between those distributions and the probability distribution of the ERA5 100 m wind speed at the same locations. This statistical relationship is called the *conditional probability distribution*.
Then there is the crucial step in the long-term correction method: we assume that this conditional probability distribution is the same in the short simulation period as in the long term. In other words: we estimate the general statistical relationship between turbine power and wind from the short simulation.
This relationship is not ‘one-to-one', in the sense that it maps one wind speed value to one power production value. Rather, it still includes all atmospheric effects of turbulence, wind direction, and stability on power production. This is because it relates one wind speed value to a distribution of power values, and the spread in this distribution is caused by the aforementioned atmospheric effects.
Finally, we integrate the statistical relation over 10 years of ERA5 wind speed, including all its interannual variability, which then gives an estimate of the 10 year AEP.

Naturally, the method is not perfect, it gives an *estimate* of the long-term power production as it would have been predicted by a long-term LES simulation. First and foremost, the quality of the estimate depends on the period simulated with the LES. Two rules of thumb: the longer it is, the better the long-term correction method works, and: the more varied it is (in terms of atmospheric conditions and weather), the better the the method works. This means that a full year, which will include many types of weather and the seasonal cycle, is good input for the long-term correction method. Based on internal research, the mean absolute error of then is about 0.4 % of the long-term AEP. The shorter the period becomes, the larger the error. For example, if 100 days are simulated, which are all roughly in the same season, the mean absolute error is in the order of 10 % of the long-term AEP.

So, our long-term correction method corrects the LES results for interannual variability of weather. Correcting the LES with in-situ observations is also possible, but this requires a more case-specific approach. For more information, feel free to send an contact Whiffle’s Consulting service at info@whiffle.nl.

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